{
 "metadata": {
  "name": "sampling"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Sampling"
     ]
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "Here are some examples on sampling techniques, mostly following C.M. Bishop's book [Pattern Recognition and Machine Learning], http://research.microsoft.com/en-us/um/people/cmbishop/PRML/. As a model task we consider the problem of sampling from a uniform distribution over square (the target distribution) if we are only allowed to sample from a Gaussian distribution (the proposal distribution).\n",
      "\n",
      "\n",
      "All the examples are implemented as demo_* functions in sampling.py."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#importing all the required stuff\n",
      "from sampling import *"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 20
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "Firstly, we describe the proposal and target distributions:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print 'Proposal distribution is N(%s, %s)'%(proposal_mean, proposal_std)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Proposal distribution is N([1.0, 1.0], [1.5, 2.0])\n"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print 'Target distribution is the uniform over the square with x_0 in [%s, %s] and x_1 in [%s, %s]'%(target_x_0[0], target_x_0[1], target_x_1[0], target_x_1[1])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Target distribution is the uniform over the square with x_0 in [-1.0, 1.0] and x_1 in [-1.0, 1.0]\n"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#plotting the proposal and target distributions\n",
      "\n",
      "#getting a sample from the proposal distribution\n",
      "proposal = proposal_sample(100)\n",
      "#plotting it\n",
      "p.scatter(proposal[:, 0], proposal[:,1], color = 'green')\n",
      "\n",
      "#plotting the bounds of the target distr\n",
      "plot_target()\n",
      "\n",
      "#setting the plotting options\n",
      "p.grid(True)\n",
      "p.xlim(target_x_0[0] - 3, target_x_0[1] + 3)\n",
      "p.ylim(target_x_1[0] - 3, target_x_1[1] + 3)\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 23,
       "text": [
        "(-4.0, 4.0)"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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t47H5fPkVcOb1mlduNXp7uXrvKrr/3B1qvRpqvRoMGIiFYswMnYnPIz6noZJW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\nwlP/B7g2qYW5+PvlAAAAAElFTkSuQmCC\n"
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Rejection sampling"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Next, we demonstrate how we can use rejection sampling to obtain a sample from the target distribution \n",
      "#if we're allowed to sample from the proposal distribution only (see demo_rejection() in sampling.py)\n",
      "\n",
      "#obtaining parameter K\n",
      "rejection_K = rejection_sampling_K()\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 24
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "Now we are ready to sample from the proposal distribution:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "size = 1000\n",
      "sample = proposal_sample(size)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 25
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "Let's check the sample's mean to ensure it corresponds to our Gaussian:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#as we see, the mean of the proposed sample is close to the center of the Gaussian\n",
      "print 'mean of the proposal sample', sample.mean(0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "mean of the proposal sample [ 1.01996352  1.05066545]\n"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "Indeed, it is close to the Gaussian's center. Next, we apply the rejection sampling to our sample:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "accepted, rejected = rejection_sampling(sample, rejection_K)\n",
      "print 'mean of the sample from the target distribution', accepted.mean(0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "mean of the sample from the target distribution [ 0.12355693  0.09337401]\n"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "Voila, the mean of the new sample is close to the mean of the target distribution. Further, we plot both samples:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#plotting the whole thing\n",
      "plot_target()\n",
      "                                                         \n",
      "#points rejected in blue\n",
      "p.scatter(rejected[:, 0], rejected[:, 1], color='blue')\n",
      "#points accepted in green\n",
      "p.scatter(accepted[:, 0], accepted[:, 1], color='green')\n",
      "\n",
      "p.grid(True)\n",
      "p.xlim(target_x_0[0] - 3, target_x_0[1] + 3)\n",
      "p.ylim(target_x_1[0] - 3, target_x_1[1] + 3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 28,
       "text": [
        "(-4.0, 4.0)"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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tWKGVngCWQ6tQIXJWQJeLky0anU8+qX+9kY9yIMAEUZK0ZbXSgBWpzNf27ZzU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2POnOz3J8sCfMWKFahevTq0Wi0OZRTN/pTjSdbEjIlhrUl6Cex2XmIeOKDcN5B+VqzImWoHD7IG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\nTkSuQmCC\n"
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "As we see from the figure above, only points within the square are accepted as a sample from the target distribution (not all of them)."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Importance sampling"
     ]
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "Another technique is importance sampling. Importance sampling estimator re-weights points generated by the proposal distribution so it can be used to estimate some statistics (e.g., mean) of the obtained sample as if it was produced from the target distribution. Importance sampling cannot be used to obtain a sample from the target distribution."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "size = 1000                                                                                                              \n",
      "\n",
      "sample = proposal_sample(size)\n",
      "weights = importance_sampling(sample)\n",
      "print 'mean of the proposal sample', sample.mean(0)\n",
      "print 'mean of the target sample', (sample * np.array([weights, weights]).T).mean(0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "mean of the proposal sample [ 0.95714009  1.13278211]\n",
        "mean of the target sample [ 0.02000702 -0.02525685]\n"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "Again, we note that the mean of the obtained sample is close to that of the targer distribution."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Importance sampling-resampling"
     ]
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "In contrast to importance sampling, importance sampling-resampling can be used to sample from the target distribution."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Further, importance sampling-resampling\n",
      "\n",
      "iterations = 100\n",
      "proposal_size = 100\n",
      "target_size = 10\n",
      "\n",
      "resample, sample = sampling_resampling(iterations, proposal_size, target_size)                                           \n",
      "print 'mean of the proposal sample', sample.mean(0)\n",
      "print 'mean of the target sample', resample.mean(0)\n",
      "print 'resample size %s, total %s'%(resample.shape[0], sample.shape[0])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "mean of the proposal sample [ 0.99981801  1.01381707]\n",
        "mean of the target sample [-0.03828051  0.04868867]\n",
        "resample size 1000, total 10000\n"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "Everything seems to be OK. Let's plot the samples."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_target()\n",
      "\n",
      "p.scatter(sample[:, 0], sample[:, 1], color='red')\n",
      "p.scatter(resample[:, 0], resample[:, 1], color='green')\n",
      "\n",
      "\n",
      "p.grid(True)\n",
      "p.xlim(target_x_0[0] - 3, target_x_0[1] + 3)\n",
      "p.ylim(target_x_1[0] - 3, target_x_1[1] + 3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 32,
       "text": [
        "(-4.0, 4.0)"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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ieY9ZMcrWrS2Z/I5BEgjQ+7BjRy3Iz6GHipx2Wno9tdtNj8wVK5gtpEULhi+4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79r362bGqdEYPRofRLjrCxkB7GrL1YUSHoybN6MrN5Gu3urcLVWEtWNN4KmTp1UyxCjmdbgwebl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\nJyJyFAuciMhRLHAiIkd9A2Z502ObpjI0AAAAAElFTkSuQmCC\n"
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "As expected, the resulting sample (green) contains points only from the rectangle."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Metropolis"
     ]
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "In our case the proposal distribution is symmetric, thus Metropolis sampling is equivalent to Metropolis-Hastings. The poposal distribution is used slightly differenently this time (see the book). Also, since the points in the sample are severely correlated, we sub-sample every 10th point before including it in the resulting sample."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "size = 10000\n",
      "sieve = [10 *k for k in xrange(1000)]\n",
      "accepted, rejected = metropolis_sampling(size)\n",
      "accepted = accepted[sieve, :]\n",
      "\n",
      "print 'mean of the resulting sample', accepted.mean(0)\n",
      "print 'accepted %s, rejected %s, total %s'%(accepted.shape[0], rejected.shape[0], size)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "mean of the resulting sample [ 0.02657611  0.02987678]\n",
        "accepted 1000, rejected 8268, total 10000\n"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "Let's plot the results:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_target()\n",
      "p.scatter(rejected[:, 0], rejected[:, 1], color='blue')\n",
      "p.scatter(accepted[:, 0], accepted[:, 1], color='green')\n",
      "\n",
      "p.grid(True)                                                                                                             \n",
      "p.xlim(target_x_0[0] - 3, target_x_0[1] + 3)\n",
      "p.ylim(target_x_1[0] - 3, target_x_1[1] + 3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 36,
       "text": [
        "(-4.0, 4.0)"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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9/HLYpjZswA5BHEzy0EPytqtchXLo0CHu0aMHf6fJ6kRETAQGoU3PuGEDmJk2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t9nVffRScqsVQsAbZXpW06Odny462etWpgro0djrrjFq09VQhcqmoYNsYMXATjRaJTfecfaADlp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\n8YVUZr5G3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+RoJr5zZZ5HlDZtoGLUMy/1XQ4b5j6ITeCGCHhV4/mcHBgihaquTRvYB0aO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\nAAAAAElFTkSuQmCC\n"
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Gibbs sampling"
     ]
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "Finally, Gibbs sampling."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "target_size = 1000\n",
      "sample = gibbs_sampling(target_size)\n",
      "\n",
      "print 'mean of the resulting sample', sample.mean(0)\n",
      "plot_target()\n",
      "p.scatter(sample[:, 0], sample[:, 1], color='green')\n",
      "p.grid(True)\n",
      "p.xlim(target_x_0[0] - 3, target_x_0[1] + 3)\n",
      "p.ylim(target_x_1[0] - 3, target_x_1[1] + 3)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "mean of the resulting sample [ 0.04906113  0.02967144]\n"
       ]
      },
      {
       "output_type": "pyout",
       "prompt_number": 37,
       "text": [
        "(-4.0, 4.0)"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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      }
     ],
     "prompt_number": 37
    }
   ],
   "metadata": {}
  }
 ]
}
